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Stochastic fluctuations and the detectability limit of network communities
Lucio Floretta1, Jonas Liechti1, Alessandro Flammini2
1Laboratoire de Biophysique Statistique, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
Summary
Network community detection limits are affected by random fluctuations. Even before networks resemble random graphs, their original structure is lost, impacting community detection accuracy.
Area of Science:
- Network Science
- Statistical Physics
- Computer Science
Background:
- Community detection algorithms aim to identify groups of nodes in networks.
- The Girvan-Newman benchmark is a standard method for evaluating community detection.
Purpose of the Study:
- To analyze the detectability limits of network communities within the Girvan-Newman benchmark.
- To investigate the impact of stochastic fluctuations on community structure.
Main Methods:
- Analysis of stochastic fluctuations in benchmark network construction.
- Development of an iterative scheme based on an infinite branching process.
- Evaluation using modularity optimization algorithms and other heuristic methods.
Main Results:
- The native network partition is lost before the in-degree/out-degree ratio matches that of Erdös-Rényi networks.
- A method was developed to estimate the true detectability limit considering fluctuations.
- Modularity optimization algorithms exhibit consistent behavior regarding the detectability threshold.
Conclusions:
- Stochastic fluctuations significantly impact the detectability of network communities.
- A precise definition of detectability limits must incorporate these random variations.
- The findings apply broadly to various community detection methods.
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